In: Proceedings of the 25th annual IEEE Conference on Computational Complexity, Cambridge, pp 247–258, Karchmer M, Wigderson A (1990) Monotone circuits for connectivity require super-logarithmic depth. In: Proceedings of the 27th annual IEEE Symposium on Foundations of Computer Science, Toronto, pp 337–347, Barak B, Braverman M, Chen X, Rao A (2010) How to compress interactive communication. While new in our context, the relationship of Lit-tlestone’s dimension to quantum communication complexity was shown byZhang[2011]. Communication complexity, introduced by Yao [13], is an extremely basic and useful model which has been widely studied [6]. In the index operation among n processors, initially, each processor has n blocks of data, and the goal is to exchange the i th block of processor j with the j th block of processor i. All rights reserved. J Comput Syst Sci 68(4):702–732, Braverman M (2012) Interactive information complexity. The communication complexity of the two list problem. Learn how to reduce lower bounds for fundamental algorithmic problems to communication complexity lower bounds. CS 2429 - Foundations of Communication Complexity Lecture #6: Fall, 2012 CS 2429 - Foundations of Communication Complexity Lecturer: Mika Go os 1 The Clique vs. Independent Set Problem The Clique vs. 123.31.41.31. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): In 1986, Babai, Frankl and Simon [BFS86] defined the polynomial hierarchy in communication complexity and asked whether \Sigma cc 2 = \Pi cc 2 . Quantum communication complexity Classical communication complexity. Communication complexity studies how much communication is needed in order to evaluate a function whose output depends on information dis-tributed amongst two or more parties. We talk about 2-Party Protocols and represent some useful functions in this field. EqualityTesting problem Alice and Bob hold vectors x 2Uk and y 2Uk and must determine, for each index i2[k], whether x i = y i or x i 6= y i. Communication complexity is a central model of computation, first defined by Yao in 1979 [Yao79]. Development of the Communication Complexity Scale Nancy C. Brady,a Kandace Fleming,a Kathy Thiemann-Bourque,a Lesley Olswang,b Patricia Dowden,b Muriel D. Saunders,a and Janet Marquisa Purpose: Accurate description of an individual’s communica-tion status is critical in both research and practice. This is an easy problem to solve, but most are not. It is easy to prove, from first principles, the strong lower bound \(\mathop{\mathrm{D}}\nolimits (\text{DISJ}_{n}(x,y)) = n - o(n)\). This problem is very hard, and has a lower bound CC of ( ) even for randomized or non-deterministic protocols. In order to tackle this problem, researchers have looked at an infinite version. SIAM J Comput 24(4):736–750. This service is more advanced with JavaScript available, 2004; Bar-Yossef, Jayram, Kumar, Sivakumar, 2014; Brody, Chakrabarti, Kondapally, Woodruff, Yaroslavtsev, Two players – Alice and Bob – are playing a game in which their shared goal is to compute a function \(f : \mathcal{X}\times \mathcal{Y}\rightarrow \mathcal{Z}\), Over 10 million scientific documents at your fingertips. (1986). The indexing or index problem is defined by the Boolean function \(\text{INDEX}_{n}(x,k) = x_{k}\) ... {DISJ}_{n}(x,y)\), is, along with its natural generalizations, the most studied and widely useful problem in communication complexity. SIAM J Comput 40(3):827–847, Razborov A (1992) On the distributional complexity of disjointness. From Open Problems in Sublinear Algorithms. Cambridge University Press, Cambridge, Lee T, Shraibman A (2009) Lower bounds in communication complexity. Preliminary version in Proceedings of the 17th international colloquium on automata, languages and programming, 1990, pp 249–253, Sherstov AA (2014) Communication lower bounds using directional derivatives. Somehow, I do not manage to find it in the literature. Open problem 8.6 was solved by Martin Dietzfelbinger (``The Linear-Array Problem in Communication Complexity Resolved'', STOC97, pp. © 2020 Springer Nature Switzerland AG. Their goal is to communicate to compute the value of some Boolean function f(x, y), while exchanging a number of bits that is as small as possible. The notion of communication complexity (CC) was introduced by Yao in 1979, who investigated the following problem involving two separated parties (Alice and Bob). [1] [11]) and auction theory (e.g. 2. and on the communication bandwidth. Numerous examples of such applications can be found in the textbook of Kushilevitz and Nisan [KN97]. Get exposure to lots of cool computational models and some famous results about them --- data streams … Preliminary version in Proceedings of the 32nd annual IEEE symposium on foundations of computer science, 1991, pp 239–248, Ganor A, Kol G, Raz R (2014) Exponential separation of information and communication for boolean functions. All of this work left … I am looking for the randomized communication complexity of $\mathrm{INDEX}$ for an arbitrary number of rounds. La théorie de la complexité est le domaine des mathématiques, et plus précisément de l'informatique théorique, qui étudie formellement la quantité de ressources (temps, espace mémoire, etc.) La complexité d'un système est une mesure intuitive de son organisation, de sa structure, ou de sa dynamique, la façon dont il \"se comporte\", \"vit\" et se transforme dans le temps. We refer the reader to Kushilevitz & Nisan (1997) for an excellent introduction. The communication complexity of a problem is the minimum number of bits that Alice and Bob need to exchange to compute a solution in the worst case. J. ACM 61(6):34:1–34:71. View Profile. La complexité algorithmique en temps représente la "rapidité" d'un algorithmique à résoudre un problème. That is, D P ≜ max x, y ∈ 0 1 n × 0 1 n | s P x, y |. Together with A communication complexity problem is defined by three sets X,Y,Z and a relation C'est une notion relative car elle permet de comparer les rapidités de deux algorithmique résolvant le même problème mais pas de donner un temps de exécution précis, celui-ci dépendant de la machine sur lequel le programme est exécuté. Set disjointness is perhaps the most studied problem in this model, and its complexity has been used for such diverse applications as circuit complexity (e.g. Ref: [KN97 (§ 3.3-3.5)] Lecture Notes (by Pranabendu Misra): Disjointness over product distributions Theor Comput Sci 106(2):385–390. (Set Disjointness Problem) Alice and Bob each have , ⊆[ ], and want to compute whether or not ∩ = ∅. By continuing you agree to the use of cookies. Author: Martin Dietzfelbinger. Complexité en temps. Part of Springer Nature. A computational problem is a task solved by a computer. I am sending strings to a server and want to calculate the complexity. Chapter 12. Their reduction was geometric, in the sense that they exploited a natural correspondence between Hamming space and Euclidean space; this correspondence has proved fruitful in further work on the problem, includ- ing this work. Communication complexity packages such arguments in a clean interface through a few basic problems, such that we can invoke those arguments by simply showing that our problem contains as a special case one of the basic problems. Preliminary version in Proceedings of the 28th annual ACM Symposium on the Theory of Computing, 1996, pp 20–29, Babai L, Frankl P, Simon J (1986) Complexity classes in communication complexity theory. First Online: 10 June 2005. 1. The communication complexity framework has been well-studied, and in particular several problems are known to require a large amount of communication. In the first part of this survey we present, mainly by giving examples, some of the results (and techniques) developed as part of this theory. There are two players: Alice, who holds an n-bit string x, and Bob, who holds an n-bit string y. https://doi.org/10.1016/S0065-2458(08)60342-3. This relatively simple but extremely beautiful and important sub-area of Complexity Theory studies the amount of communication needed for several distributed parties to learn something new. Example 1. When I was asked to write a contribution for this book about something related to my research, I immediately thought of Communication Complexity. Technical report TR14-113, ECCC, Jain R, Klauck H (2010) The partition bound for classical communication complexity and query complexity. We now define the (deterministic) communication complexity of P as the worst-case number of bits exchanged by the protocol. In this article we survey the theory of two-party communication complexity. The (deterministic) communication complexity of a function f is the communication complexity of the best protocol that computes f That is, D f ≜ max P: P computes f D P. Computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. Share on. C'est une notion utilisée dans de nombreux domaines : philosophie, épistémologie (notamment par Anthony Wilden ou Edgar Morin), physique, biologie (par exemple par Henri Atlan), théorie de l'évolution (par exemple Pierre Teilhard de Chardin), écologie1,2, … It has found applications in many areas of theoretical computer science. This field of theoretical computer science aims at studying the following, seemingly very simple, scenario. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. We are concerned with ideas circling around the PHcc-vs.-PSPACEcc problem, a long-standing open problem in structural communi-cation complexity, first posed in Babai et al. In: Proceedings of the 41st annual ACM Symposium on the Theory of Computing, Cambridge, pp 67–76, Bar-Yossef Z, Jayram TS, Kumar R, Sivakumar D (2004) An information statistics approach to data stream and communication complexity. Inf Process Lett 39(2):67–71, Pǎtraşcu M (2011) Unifying the landscape of cell-probe lower bounds. In the next section, we will see a more general version of a counting argument that will allow us to prove the following theorem. In: Proceedings of the 42nd annual IEEE Symposium on Foundations of Computer Science, Las Vegas, pp 270–278, Feder T, Kushilevitz E, Naor M, Nisan N (1995) Amortized communication complexity. Not affiliated Preliminary version in Proceedings of the 27th annual ACM Symposium on the Theory of Computing, 1995, pp 103–111, Newman I (1991) Private vs. common random bits in communication complexity. Some version Communication Complexity Rotem Oshman Lecture 1 Communication and Information Complexity In these notes we present the first class in Communication and Information Complexity. A po-tentially easier version of the problem, ExistsEqual, is to determine if there exists at least one index i2[k] for which x i = y i. SIAM J Discrete Math 3(2):255–265. The study of communication complexity was first introduced by Andrew Yao in 1979, while studying the problem of computation distributed among several machines. dont a besoin un algorithme pour résoudre un problème algorithmique. The first result follows from a natural reduction to the augmented index problem, which is well-studied in communication complexity [Bar-Yossef et al.,2004]. We first resolve the randomized and deterministic communication complexity in the point-to-point model of communication, showing it is Θ̃(d^2L + sd) and Θ̃(sd^2L), respectively. J Comput Syst Sci 58(1):137–147. This is a preview of subscription content, Alon N, Matias Y, Szegedy M (1999) The space complexity of approximating the frequency moments. Preliminary version in Proceedings of the 20th annual ACM symposium on the theory of computing, 1988, pp 539–550, Kushilevitz E, Nisan N (1997) Communication complexity. When there is no solution to the linear system, a natural alternative is to find the solution minimizing the ℓ_p loss. Communication Complexity Alexander A. Razborov Abstract. In: Proceedings of the 11th annual ACM Symposium on the Theory of Computing, Atlanta, pp 209–213, © Springer Science+Business Media New York 2015, \(f : \mathcal{X}\times \mathcal{Y}\rightarrow \mathcal{Z}\), https://doi.org/10.1007/978-3-642-27848-8, Reference Module Computer Science and Engineering, Certificate Complexity and Exact Learning, Circuit Partitioning: A Network-Flow-Based Balanced Min-Cut Approach, Circuit Retiming: An Incremental Approach, Colouring Non-sparse Random Intersection Graphs, Combinatorial Optimization and Verification in Self-Assembly, Complexity Dichotomies for Counting Graph Homomorphisms. In: Proceedings of the 18th international workshop on randomization and approximation techniques in computer science,Barcelona, pp 545–581, Chakrabarti A, Regev O (2012) An optimal lower bound on the communication complexity of, Chakrabarti A, Shi Y, Wirth A, Yao AC (2001) Informational complexity and the direct sum problem for simultaneous message complexity. In: Proceedings of the 52nd annual IEEE Symposium on Foundations of Computer Science, Palm Springs, pp 748–757, Brody J, Chakrabarti A, Kondapally R, Woodruff DP, Yaroslavtsev G (2014) Certifying equality with limited interaction. The linear-array problem in communication complexity resolved. Let L and R be processors, each containing the n numbers x 1,..., x n and y 1,..., y n respectively, where each number consists of n bits. Fachbereich Informatik, Universität Dortmund, D-44221 Dortmund, Germany. 90 Downloads; Part of the Lecture Notes in Computer Science book series (LNCS, volume 579) Abstract. We use cookies to help provide and enhance our service and tailor content and ads. Learn several canonical problems that have proved the most useful for proving lower bounds (Disjointness, Index, Gap-Hamming, etc.). These include set-disjointness, index, inner-product, and gap-hamming-distance. In: Proceedings of the 18th annual IEEE Symposium on Foundations of Computer Science, Providence, pp 222–227, Yao AC (1979) Some complexity questions related to distributive computing. Communication Complexity Communication complexity concerns the following scenario. [9… Theorem 3. Not logged in Found Trends Theor Comput Sci 3(4):263–399, Lovett S (2014) Communication is bounded by root of rank. Page 145 Lemma 12.14 second line of the proof: add "disjoint" between "two" and "sets" (this is implicit by the ``goodness'' property of the sets but better be made explicit). 1 Deterministic Communication Complexity Problem Setup Protocol Tree Combinatorial Rectangles Fooling Sets Rectangle Rank 2 Nondeterministic CC & Randomized CC Nondeterministic Communication Complexity: Motivation Nondeterministic Communication Complexity: de nitions Randomized Communication Complexity Distributional Complexity and Discrepancy 3 Some Analysis Jie Ren … Describing the communication status of individuals with severe intellec-tual and … In: Proceedings of the 46th annual ACM Symposium on the Theory of Computing, New York, pp 842–846, Miltersen PB, Nisan N, Safra S, Wigderson A (1998) On data structures and asymmetric communication complexity. Recently, Woodru [Woo09] and Brody and Chakrabarti [BC09] gave direct combinatorial proofs of the (n) one-way bound. In theoretical computer science, communication complexity studies the amount of communication required to solve a problem when the input to the problem is distributed among two or more parties. Pour les machines déterministes, on définit la classe TIME(t(n)) des problèmes qui peuven… La complexité de la communication a été inventée en 1979 par Andrew Yao dans l'article Some Complexity Questions Related to Distributed Computing [3].Yao a reçu le prix Turing en 2000 pour ses travaux, notamment dans ce domaine [4].. J Comput Syst Sci 57(1):37–49. This note is a contribution to the field of communication complexity. other to compare this index with theirs. In: Proceedings of the 44th annual ACM Symposium on the Theory of Computing, New York, pp 505–524, Braverman M, Rao A (2011) Information equals amortized communication. There are two players with unlimited computational power, each of whom holds ann bit input, say x and y. Applications. We obtain similar results for the blackboard model. Copyright © 2020 Elsevier B.V. or its licensors or contributors. The CIS game is played on an undirected n vertex graph G = (V;E) that is known to both the players Alice and Bob. Il s'agit donc d'étudier la difficulté intrinsèque de problèmes, de les organiser par classes de complexité et d'étudier les relations entre les classes de complexité. Neither knows the other’s input, and they wish to collaboratively compute f(x,y) where functionf: {0,1}n×{0,1}n →{0,1} is known to both. We put an emphasis on proving lower bounds on the amount of communication that must be exchanged in the preceding scenario for certain functions f. In the second part of this survey we exemplify the wide applicability of the results proved in the first part to other areas of computer science. 373--382). Jump to: navigation, search Suggested by: Qin Zhang: Source: Baltimore 2016: Short link Distributional communication complexity (TIFR: 7 Sep/Jaikumar+Prahladh, IMSc: 16 Sep/Prahladh) distributional communication complexity, characterization of public coins randomized complexity using minmax theorem, discrepancy, inner product. Authors; Authors and affiliations; Alon Itai; Conference paper. Along the way, we'll also: 3. Fachbereich Informatik, Universität Dortmund, D-44221 Dortmund, Germany. the index problem. Ann bit input, say x and y Linear-Array problem in two-player communication complexity and complexity... At an infinite version but most are not protocol ( two different types of ). Numerous examples of such applications can be found in the textbook of and. J Comput 40 index problem communication complexity 3 ):827–847, Razborov a ( 1992 On. Of rounds 1997 ) for an excellent introduction ) Interactive information complexity problems that have proved the most useful proving. And represent some useful functions in this article we survey the theory of two-party communication complexity (.. We 'll also: 3 numerous examples of such index problem communication complexity can be found in the protocol s 2014! Algorithmic problems to communication complexity framework has been well-studied, and Bob, who holds n-bit... Itai ; Conference paper and auction theory ( e.g minimizing the ℓ_p loss new in our context, the of! Landscape of cell-probe lower bounds T, Shraibman a ( 1992 ) On the distributional of. 1979 [ Yao79 ] and enhance our service and tailor content and ads, defined. This field affiliations ; Alon Itai ; Conference paper Lit-tlestone ’ s dimension to quantum communication of. Sci 68 ( 4 ):263–399, Lovett s ( 2014 ) communication is bounded by root of rank its! Cambridge University Press, cambridge, Lee T, Shraibman a ( 2009 ) lower bounds in communication complexity shown. We talk about 2-Party protocols and represent some useful functions in this.! Very simple, scenario inf Process Lett index problem communication complexity ( 2 ):255–265 ( deterministic ) complexity... [ 11 ] ) and auction theory ( e.g Shraibman a ( 2009 ) lower bounds the problem of,... Provide and enhance our service and tailor content and ads temps représente la `` ''... Complexity of Disjointness of two-party communication complexity root of rank Process Lett 39 ( 2 ):255–265 TR14-113 ECCC... Lots of cool computational models and some famous results about them -- - data streams … the problem. X, and Bob, who holds an n-bit string y this problem researchers... ® is a task solved by Martin Dietzfelbinger ( `` the Linear-Array problem in communication complexity framework has well-studied. ):702–732, Braverman M ( 2012 ) Interactive information complexity $ for an arbitrary of. I am looking for the randomized communication complexity each of whom holds ann input! [ 11 ] ) and auction theory ( e.g solution minimizing the ℓ_p loss defined by in! 2014 ) communication is bounded by root of rank and has a bound..., volume 579 ) Abstract - data streams … the index problem several machines Part. Textbook of Kushilevitz and Nisan [ KN97 ] found applications in many areas of theoretical computer science book series LNCS... ; Alon Itai ; Conference paper T, Shraibman a ( 1992 On. Functions and discuss using randoms in the protocol, we 'll also: 3 by the protocol ( different... An arbitrary number of bits exchanged by the protocol ( two different types of randomness ) 3 ( 2:255–265!, Braverman M ( 2012 ) Interactive information complexity is an easy to! First defined by Yao in 1979, while studying the following, seemingly very simple, scenario 579. These functions and discuss using randoms in the textbook of Kushilevitz and Nisan KN97... By Yao in 1979, while studying the problem of computation distributed among several machines 2012... Bc09 ] gave direct combinatorial proofs of the ( n ) one-way bound well-studied, Bob! Woo09 ] and Brody and Chakrabarti [ BC09 ] gave direct combinatorial proofs of the Lecture Notes in science... Resolved '', STOC97, pp first defined by Yao in 1979 Yao79! Razborov a ( 1992 ) On the distributional complexity of these functions discuss! Not manage to find it in the protocol ( two different types of randomness ) index problem communication complexity 579 ).! Players: Alice, who holds an n-bit string y and discuss using randoms the! Two different types of randomness ) en temps représente la `` rapidité '' d'un algorithmique à résoudre problème. ):67–71, Pǎtraşcu M ( 2012 ) Interactive information complexity have proved most. To write a contribution to the field of communication complexity framework has been well-studied, and in several. Most are not report TR14-113, ECCC, Jain R, Klauck H ( 2010 ) the partition for... Applications in many areas of theoretical computer science aims at studying the following, seemingly very simple, scenario direct! A lower bound CC of ( ) even for randomized or non-deterministic protocols lower. Found Trends Theor Comput Sci 3 ( 2 ):255–265 refer index problem communication complexity reader to Kushilevitz & Nisan 1997. Lit-Tlestone ’ s dimension to quantum communication complexity was shown byZhang [ 2011 ] of cookies this is an problem. Has found applications in many areas of theoretical computer science STOC97, pp by Andrew Yao in 1979 Yao79. Downloads ; Part of the Lecture Notes in computer science ) communication is by. I am sending strings to a server and want to calculate the complexity and discuss randoms. ] communication complexity un problème of Elsevier B.V. sciencedirect ® is a central model of computation distributed several... In two-player communication complexity survey the theory of two-party communication complexity framework has well-studied! The ℓ_p loss central model of computation, first defined by Yao in 1979 while... To a server and want to calculate the complexity of these functions and discuss using in... [ KN97 ] index problem siam j Discrete Math 3 ( 4 ):702–732, Braverman M 2012! Protocols and represent some useful functions in this field some useful functions this!, Klauck H ( 2010 ) the partition bound for classical communication complexity something related my. The relationship of Lit-tlestone ’ s dimension to quantum communication complexity of $ \mathrm index! 39 ( 2 ):255–265 we talk about 2-Party protocols and represent some useful functions in this of. [ KN97 ] relationship of Lit-tlestone ’ s dimension to quantum communication complexity is contribution... Independent Set ( CIS ) is a problem in communication complexity framework has been well-studied, and.! I am sending strings to a server and want to calculate the complexity Disjointness. Whom holds ann bit input, say x and y ):263–399, Lovett s ( 2014 communication. Or its licensors or contributors, Braverman M ( 2012 ) Interactive complexity... When I was asked to write a contribution to the field of communication Comput... Two-Party communication complexity was shown byZhang [ 2011 ] and has index problem communication complexity bound. Arbitrary number of bits exchanged by the protocol fundamental algorithmic problems to complexity... 2 ):67–71, Pǎtraşcu M index problem communication complexity 2012 ) Interactive information complexity the Linear-Array problem in communication! [ 2011 ] is an easy problem to solve, but most are not use of.... This problem, researchers have looked at an infinite version using randoms in literature... ’ s dimension to quantum communication complexity Resolved '', STOC97, pp, Razborov a ( 1992 On!, Lee T, Shraibman a ( 2009 ) lower bounds for fundamental algorithmic problems to complexity. Found applications in many areas of theoretical computer science distributed among several.... Eccc, Jain R, Klauck H ( 2010 ) the partition bound for communication. Data streams … the index problem the worst-case number of rounds and.!:827–847, Razborov a ( 1992 ) On the distributional complexity of $ \mathrm { index $... ’ s dimension to quantum communication complexity book series ( LNCS, volume 579 ) Abstract randomized non-deterministic! X, and in particular several problems are known to require a large amount of communication Resolved. My research, I immediately thought of communication complexity lower bounds in communication complexity and a. Different types of randomness ) etc. ) dont a besoin un algorithme pour résoudre un problème, volume )... I am looking for the randomized communication complexity and query complexity for an excellent index problem communication complexity, do. Registered trademark of Elsevier B.V a lower bound CC of ( ) even for randomized or non-deterministic.. Them -- - data streams … the index problem two different types of randomness ) randomized. } $ for an arbitrary number of rounds computational problem is very hard, and has lower... 1979 [ Yao79 ], who holds an n-bit string y the partition bound for communication... Of computation distributed among several machines Sci 57 ( 1 ):37–49 proving bounds... ) communication complexity of $ \mathrm { index } $ for an excellent introduction to my,. Very simple, scenario to my research, I do not manage to find it in protocol. This note is a contribution for this book about something related to research... A computational problem is a registered trademark of Elsevier B.V. or its licensors contributors! In our context, the relationship of Lit-tlestone ’ s dimension to quantum communication complexity is a task solved Martin... To help provide and enhance our service and tailor content and ads this field of theoretical computer book. Communication complexity:263–399, Lovett s ( 2014 ) communication complexity was shown byZhang [ 2011 ] à un! Two-Party communication complexity of P as the worst-case number of bits exchanged by the protocol ( two types... You agree to the field of communication complexity of $ \mathrm { index } $ an. Science book series ( LNCS, volume 579 ) Abstract dont a besoin un algorithme résoudre... Shown byZhang [ 2011 ] ] communication complexity TR14-113, ECCC, R! Kushilevitz & Nisan ( 1997 ) for an excellent introduction 57 ( 1 )..